Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: A statistical model

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types-each one associated, respectively, with the polar-headgroup and the acyl-chain states-which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.

Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

Probability currents and entropy production in nonequilibrium lattice systems

The structure of probability currents is studied for the dynamical network after consecutive contraction on two-state, nonequilibrium lattice systems. This procedure allows us to investigate the transition rates between configurations on small clusters and highlights some relevant effects of lattice symmetries on the elementary transitions that are responsible for entropy production. A method is suggested to estimate the entropy production for different levels of approximations (cluster sizes) as demonstrated in the two-dimensional contact process with mutation.

Statistical models of mixtures with a biaxial nematic phase

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rodlike and disklike molecules. A quenched distribution of shapes leads to a phase diagram with two uniaxial and a biaxial nematic structure. A thermalized distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.

Generalized Sznajd model for opinion propagation

In the last decade the Sznajd model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a version of the Sznajd model with a generalized bounded confidence rule-a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabaacutesi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.

Coexistence of interacting opinions in a generalized Sznajd model

The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favor groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and, although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, which has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviors, we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model by generalizing the bounded confidence rule, which is common to many continuous opinion models, to what we called confidence rules. In that work we have found that the mean field version of this model (corresponding to a complete network) allows for stationary states where noninteracting opinions survive, but never for the coexistence of interacting opinions. In the present work, we provide networks that allow for the coexistence of interacting opinions for certain confidence rules. Moreover, we show that the model does not become inactive; that is, the opinions keep changing, even in the stationary regime. This is an important result in the context of understanding how a rule that breeds local conformity is still able to sustain global diversity while avoiding a frozen stationary state. We also provide results that give some insights on how this behavior approaches the mean field behavior as the networks are changed.

Role of noise in population dynamics cycles

Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems. Langevin equations in the population densities and predator-prey pair density are derived in two stages. First, a birth-and-death stochastic process in the space of prey and predator numbers and predator-prey pair number is obtained by a contraction method that reduces the degrees of freedom. Second, a van Kampen expansion in the inverse of system size is then performed to get the Fokker-Planck equation. We also study the time correlation function, the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence.

Thermodynamic origin of cooperativity in actomyosin interactions: The coupling of short-range interactions with actin bending stiffness in an Ising-like model

We present Monte Carlo simulations for a molecular motor system found in virtually all eukaryotic cells, the acto-myosin motor system, composed of a group of organic macromolecules. Cell motors were mapped to an Ising-like model, where the interaction field is transmitted through a tropomyosin polymer chain. The presence of Ca(2+) induces tropomyosin to block or unblock binding sites of the myosin motor leading to its activation or deactivation. We used the Metropolis algorithm to find the transient and the equilibrium states of the acto-myosin system composed of solvent, actin, tropomyosin, troponin, Ca(2+), and myosin-S1 at a given temperature, including the spatial configuration of tropomyosin on the actin filament surface. Our model describes the short- and long-range cooperativity during actin-myosin binding which emerges from the bending stiffness of the tropomyosin complex. We found all transition rates between the states only using the interaction energy of the constituents. The agreement between our model and experimental data also supports the recent theory of flexible tropomyosin.

Missing levels in acoustic resonators

It is shown that the deviations of the experimental statistics of six chaotic acoustic resonators from Wigner-Dyson random matrix theory predictions are explained by a recent model of random missing levels. In these resonatorsa made of aluminum plates a the larger deviations occur in the spectral rigidity (SRs) while the nearest-neighbor distributions (NNDs) are still close to the Wigner surmise. Good fits to the experimental NNDs and SRs are obtained by adjusting only one parameter, which is the fraction of remaining levels of the complete spectra. For two Sinai stadiums, one Sinai stadium without planar symmetry, two triangles, and a sixth of the three-leaf clover shapes, was found that 7%, 4%, 7%, and 2%, respectively, of eigenfrequencies were not detected.

Power-law creep behavior of a semiflexible chain

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Time correlation function in systems with two coexisting biological species

We study a stochastic lattice model describing the dynamics of coexistence of two interacting biological species. The model comprehends the local processes of birth, death, and diffusion of individuals of each species and is grounded on interaction of the predator-prey type. The species coexistence can be of two types: With self-sustained coupled time oscillations of population densities and without oscillations. We perform numerical simulations of the model on a square lattice and analyze the temporal behavior of each species by computing the time correlation functions as well as the spectral densities. This analysis provides an appropriate characterization of the different types of coexistence. It is also used to examine linked population cycles in nature and in experiment.

Frustration and anomalous behavior in the Bell-Lavis model of liquid water

We have reconsidered the Bell-Lavis model of liquid water and investigated its relation to its isotropic version, the antiferromagnetic Blume-Emery-Griffiths model on the triangular lattice. Our study was carried out by means of an exact solution on the sequential Husimi cactus. We show that the ground states of both models share the same topology and that fluid phases (gas and low- and high-density liquids) can be mapped onto magnetic phases (paramagnetic, antiferromagnetic, and dense paramagnetic, respectively). Both models present liquid-liquid coexistence and several thermodynamic anomalies. This result suggests that anisotropy introduced through orientational variables play no specific role in producing the density anomaly, in agreement with a similar conclusion discussed previously following results for continuous soft core,models. We propose that the presence of liquid anomalies may be related to energetic frustration, a feature common to both models.

Experimental observation of a complex periodic window

The existence of a special periodic window in the two-dimensional parameter space of an experimental Chua's circuit is reported. One of the main reasons that makes such a window special is that the observation of one implies that other similar periodic windows must exist for other parameter values. However, such a window has never been experimentally observed, since its size in parameter space decreases exponentially with the period of the periodic attractor. This property imposes clear limitations for its experimental detection.

Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.